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The average kinetic energy of one molecule of an ideal gas at 27C and 1atm pressure is:
[A] 900 cal K1mol1
[B] 6.21×1021J K1moleculee1
[C] 336.7J K1moleculee1
[D] 3741.3 J K1mol1


Answer
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HINT: The average kinetic energy if dependent only upon the temperature. You can solve this by using the formula- K.E=32KBT, where the terms have their usual meanings. Do not forget that the Boltzmann constant can be written as- KB=RNA.

COMPLETE STEP BY STEP SOLUTION: We know that the kinetic energy of a particle is the energy that it possesses due to motion. We define it as the work needed to accelerate a body of a certain given mass from rest.
According to the kinetic theory of gases, we can find the average kinetic energy of per molecule any particle by the formula-
     K.E=32KBT
Where, KB is Boltzmann's constant, T is the temperature and K.E is the average kinetic energy.
We can also rewrite the above formula for per mole of a gas as-
     K.E=32nRT
Where, n is the number of moles of the particular gas, T is the temperature, R is the universal gas constant whose value is fixed and K.E is the average kinetic energy.
Now, for one molecule of ideal gas, we can write the first formula as-
     K.E=32RTNA
We know that Boltzmann’s constant KB=RNA
Where, NA is Avogadro's number.
Now in the question the temperature is given as 27C but we have to convert it in kelvin. We know that 0C is equal to 273 K.
Therefore, 27C is 27 + 273 K = 300K.
The value of the universal gas constant, R = 8.314 J/Kmol
And we know that the value of Avogadro’s number, NA= 6.022×1023
Now we will put these values in the average kinetic energy equation to find out its value for one molecule of an ideal gas.
     K.E=32×8.314 J/Kmol×300K6.022×1023=6.21×1021J/molecule
We can see from the above calculation that the value of average kinetic energy for one molecule of an ideal gas is 6.21×1021J/molecule.


Therefore the correct answer is option [B] 6.21×1021J K1moleculee1

NOTE: The average kinetic energy of a particle is dependent only upon the absolute temperature of the system. The absolute temperature is a scale for measurement of temperature of an object where 0 is taken as absolute zero. The absolute temperature scales are kelvin and Rankine.


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